When I load a file, if it has 4-space indents, I want them to behave like tabs (so that if I hit the left/right arrow keys across those 4 spaces, it moves the cursor 4 spaces as if it's a tab, or at least goes to the beginning or end of the indent), but save as 4 spaces.

If you hit the Home keyboard button, the cursor will go to the beginning of the line (column 0). Hitting Home again, moves the cursor to the end of the indentation (beginning of the actual code on the line). Hitting Home again moves the cursor to column 0 and so on...

Also try keeping Ctrl pressed while hitting Left and Right arrow keys. This will move the cursor at the beginning and at the end of the indentation.